Information on Result #895797
Linear OOA(4244, 4194311, F4, 2, 26) (dual of [(4194311, 2), 8388378, 27]-NRT-code), using (u, u+v)-construction based on
- linear OOA(415, 10, F4, 2, 13) (dual of [(10, 2), 5, 14]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,6P) [i] based on function field F/F4 with g(F) = 2 and N(F) ≥ 10, using
- linear OOA(4229, 4194301, F4, 2, 26) (dual of [(4194301, 2), 8388373, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4229, 8388602, F4, 26) (dual of [8388602, 8388373, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4229, large, F4, 26) (dual of [large, large−229, 27]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,25], and designed minimum distance d ≥ |I|+1 = 27 [i]
- discarding factors / shortening the dual code based on linear OA(4229, large, F4, 26) (dual of [large, large−229, 27]-code), using
- OOA 2-folding [i] based on linear OA(4229, 8388602, F4, 26) (dual of [8388602, 8388373, 27]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(4244, 4194311, F4, 3, 26) (dual of [(4194311, 3), 12582689, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (218, 244, 4194311)-net over F4 | [i] | ||